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arXiv:1310.2428v1 [astro-ph.EP] 9 Oct 2013
DRAFT VERSION OCTOBER 10, 2013
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A SUPER-JUPITER ORBITING A LATE-TYPE STAR: A REFINED ANALYSIS OF MICROLENSING EVENT
OGLE-2012-BLG-0406.
Y. TSAPRAS1,R1,♠, J.-Y. CHOIK1, R. A. STREET1,♠, C. HANK1,⋆,‡, V. BOZZAN3,♦, A. GOULDU1,‡, M. DOMINIK∗R3,♦,♠,♣, J.-P.
BEAULIEUP4,♣, A. UDALSKIO1,, U. G. JØRGENSENN1,♦, T. SUMIM1,†,
AND
D. M. BRAMICHR2,R6, P. BROWNER3,♦, K. HORNER3,♣, M. HUNDERTMARKR3,♦, S. IPATOVN2, N. KAINSR2,♦, C. SNODGRASSR5,♦, I. A.
STEELER4,
(THE ROBONET COLLABORATION),
K. A. ALSUBAIN2, J. M. ANDERSENN9, S. CALCHI NOVATIN3,N18, Y. DAMERDJIN8, C. DIEHLN15,N17, A. ELYIVN8,N19, E. GIANNININ15, S.
HARDISN1, K. HARPSØEN5, T. C. HINSEN1,N10,N11, D. JUNCHERN1, E. KERINSN12, H. KORHONENN1, C. LIEBIGR3, L. MANCININ13, M.
MATHIASENN1, M. T. PENNYU1, M. RABUSN14, S. RAHVARN6, G. SCARPETTAN3,N4,N16, J. SKOTTFELTN1,N5, J. SOUTHWORTHN7, J.
SURDEJN8, J. TREGLOAN-REEDN7, C. VILELAN7, J. WAMBSGANSSN15
(THE MINDSTEPCOLLABORATION),
S. KOZŁOWSKIO1, M. KUBIAKO1, P. PIETRUKOWICZO1, G. PIETRZY ´ NSKIO1,O2, R. POLESKIO1,U1, J. SKOWRONO1, I. SOSZY ´ NSKIO1, M. K.
SZYMA ´ NSKIO1, K. ULACZYKO1, ŁUKASZ WYRZYKOWSKIO1,O3
(THE OGLE COLLABORATION),
M. D. ALBROWP1, E. BACHELETP2,P3, R. BARRYP11, V. BATISTAP4, A. BHATTACHARYAM10, S. BRILLANTP5, J. A. R. CALDWELLP6, A.
CASSANP4, A. COLEP7, E. CORRALESP4, CH. COUTURESP4, S. DIETERSP2, D. DOMINIS PRESTERP8, J. DONATOWICZP9, P.
FOUQUÉP2,P3, J. GREENHILLP7, S. R. KANEP10, D. KUBASP4,P5, J.-B. MARQUETTEP4, J. MENZIESP12, K. R. POLLARDP1, D. WOUTERSP4
(THE PLANET COLLABORATION),
G. CHRISTIEU6, D. L. DEPOYU2, S. DONGU3, J. DRUMMONDU9, B. S. GAUDIU1, C. B. HENDERSONU1, K. H. HWANGK1, Y. K. JUNGK1,
A. KAVKAU1, J.-R. KOOU4, C.-U. LEEU4, D. MAOZU10, L. A. G. MONARDU5, T. NATUSCHU6, H. NGANU6, H. PARKK1, R. W. POGGEU1,
I. PORRITTU7, I.-G. SHINK1, Y. SHVARTZVALDU10, T. G. TANU8, J. C. YEEU1
(THE µFUN COLLABORATION),
F. ABEM2, D. P. BENNETTM10, I. A. BONDM3, C. S. BOTZLERM4, M. FREEMANM4, A. FUKUIM6, D. FUKUNAGAM2, Y. ITOWM2, N.
KOSHIMOTOM1, C. H. LINGM3, K. MASUDAM2, Y. MATSUBARAM2, Y. MURAKIM2, S. NAMBAM1, K. OHNISHIM7, N. J. RATTENBURYM4,
TO. SAITOM8, D. J. SULLIVANM5, W. L. SWEATMANM3, D. SUZUKIM1, P. J. TRISTRAMM9, N. TSURUMIM2, K. WADAM1, N. YAMAIM11,
P. C. M. YOCKM4A. YONEHARAM11
(THE MOA COLLABORATION)
1Las Cumbres Observatory Global Telescope Network, 6740 Cortona Drive, suite 102, Goleta, CA 93117, USA
K1Department of Physics, Chungbuk National University, Cheongju 361-763, Republic of Korea
R1School of Physics and Astronomy, Queen Mary University of London, Mile End Road, London E1 4NS, UK
R2European Southern Observatory, Karl-Schwarzschild-Str. 2, 85748 Garching bei München, Germany
R3SUPA, School of Physics & Astronomy, University of St Andrews, North Haugh, St Andrews KY16 9SS, UK
R4Astrophysics Research Institute, Liverpool John Moores University, Liverpool CH41 1LD, UK
R5Max Planck Institute for Solar System Research, Max-Planck-Str. 2, 37191 Katlenburg-Lindau, Germany
R6Qatar Environment and Energy Research Institute, Qatar Foundation, Tornado Tower, Floor 19, P.O. Box 5825, Doha, Qatar
N1Niels Bohr Institute, Astronomical Observatory, Juliane Maries vej 30, 2100 Copenhagen, Denmark
N2Qatar Foundation, P.O. Box 5825, Doha, Qatar
N3Dipartimento di Fisica “E. R. Caianiello”, Università di Salerno, Via Giovanni Paolo II n. 132, 84084 Fisciano (SA), Italy
N4International Institute for Advanced Scientific Studies (IIASS), 84019 Vietri sul Mare, (SA), Italy
N5Centre for Star and Planet formation, Geological Museum, Øster Voldgade 5, 1350, Copenhagen, Denmark
N6Dept. of Physics, Sharif University of Technology, P.O. Box 11155-9161, Tehran, Iran
N7Astrophysics Group, Keele University, Staffordshire, ST5 5BG, UK
N8Institut d’Astrophysique et de Géophysique, Allée du 6 Août 17, Sart Tilman, Bât. B5c, 4000 Liége, Belgium
N9Boston University, Astronomy Department, 725 Commonwealth Avenue, Boston, MA 02215, USA
N10Armagh Observatory, College Hill, Armagh, BT61 9DG, Northern Ireland, UK
N11Korea Astronomy and Space Science Institute, 776 Daedukdae-ro, Yuseong-gu, Daejeon 305-348, Korea
N12Jodrell Bank Centre for Astrophysics, University of Manchester, Oxford Road,Manchester, M13 9PL, UK
N13 Max Planck Institute for Astronomy, Königstuhl 17, 69117 Heidelberg, Germany
N14 Instituto de Astrofísica, Facultad de Física, Pontificia Universidad Católica de Chile, Av. Vicuña Mackenna 4860, 7820436 Macul, Santiago, Chile
N15Astronomisches Rechen-Institut, Zentrum für Astronomie der Universität Heidelberg (ZAH), Mönchhofstr. 12-14, 69120 Heidelberg, Germany
N16INFN, Gruppo Collegato di Salerno, Sezione di Napoli, Italy
N17Hamburger Sternwarte, Universität Hamburg, Gojenbergsweg 112, 21029 Hamburg, Germany
N18Istituto Internazionale per gli Alti Studi Scientifici (IIASS),84019 Vietri Sul Mare (SA), Italy
N19Main Astronomical Observatory, Academy of Sciences of Ukraine, vul. Akademika Zabolotnoho 27, 03680 Kyiv, Ukraine
O1Warsaw University Observatory, Al. Ujazdowskie 4, 00-478 Warszawa, Poland
O2Universidad de Concepción, Departamento de Astronomia, Casilla 160-C, Concepción, Chile
O3Institute of Astronomy, University of Cambridge, Madingley Road, Cambridge CB3 0HA, UK
P1University of Canterbury, Dept. of Physics and Astronomy, Private Bag 4800, 8020 Christchurch, New Zealand
P2Université de Toulouse, UPS-OMP, IRAP, 31400 Toulouse, France
P3CNRS, IRAP, 14 avenue Edouard Belin, 31400 Toulouse, France
P4UPMC-CNRS, UMR7095, Institut d’Astrophysique de Paris, 98bis boulevard Arago, 75014 Paris, France
P5European Southern Observatory (ESO), Alonso de Cordova 3107, Casilla 19001, Santiago 19, Chile
P6McDonald Observatory, 16120 St Hwy Spur 78 #2, Fort Davis, TX 79734, USA
P7School of Math and Physics, University of Tasmania, Private Bag 37, GPO Hobart, 7001 Tasmania, Australia

2 A REFINED ANALYSIS OF MICROLENSING EVENT OGLE-2012-BLG-0406
P8Physics Department, Faculty of Arts and Sciences, University of Rijeka, Omladinska 14, 51000 Rijeka, Croatia
P9Technical University of Vienna, Department of Computing, Wiedner Hauptstrasse 10, Vienna, Austria
P10Department of Physics & Astronomy, San Francisco State University, 1600 Holloway Avenue, San Francisco, CA 94132, USA
P11Laboratory for Exoplanets and Stellar Astrophysics, Mail Code 667, NASA/GSFC, Bldg 34, Room E317, Greenbelt, MD 20771
P12South African Astronomical Observatory, PO Box 9, Observatory 7935, South Africa
U1Department of Astronomy, Ohio State University, 140 West 18th Avenue, Columbus, OH 43210, USA
U2Department of Physics and Astronomy, Texas A&M University, College Station, TX 77843, USA
U3Institute for Advanced Study, Einstein Drive, Princeton, NJ 08540, USA
U4Korea Astronomy and Space Science Institute, Daejeon 305-348, Republic of Korea
U5Klein Karoo Observatory, Calitzdorp, and Bronberg Observatory, Pretoria, South Africa
U6Auckland Observatory, Auckland, New Zealand
U7Turitea Observatory, Palmerston North, New Zealand
U8Perth Exoplanet Survey Telescope, Perth, Australia
U9Possum Observatory, Patutahi, Gisbourne, New Zealand
U10 School of Physics and Astronomy, Tel-Aviv University, Tel-Aviv 69978, Israel
M1Department of Earth and Space Science, Osaka University, Osaka 560-0043, Japan
M2Solar-Terrestrial Environment Laboratory, Nagoya University, Nagoya, 464-8601, Japan
M3Institute of Information and Mathematical Sciences, Massey University, Private Bag 102-904, North Shore Mail Centre, Auckland, New Zealand
M4Department of Physics, University of Auckland, Private Bag 92-019, Auckland 1001, New Zealand
M5School of Chemical and Physical Sciences, Victoria University, Wellington, New Zealand
M6Okayama Astrophysical Observatory, National Astronomical Observatory of Japan, Asakuchi, Okayama 719-0232, Japan
M7Nagano National College of Technology, Nagano 381-8550, Japan
M8Tokyo Metropolitan College of Aeronautics, Tokyo 116-8523, Japan
M9Mt. John University Observatory, P.O. Box 56, Lake Tekapo 8770, New Zealand
M10University of Notre Dame, Department of Physics, 225 Nieuwland Science Hall, Notre Dame, IN 46556-5670, USA
M11Department of Physics, Faculty of Science, Kyoto Sangyo University, 603-8555, Kyoto, Japan
♠The RoboNet Collaboration
♦The MiNDSTEp Collaboration
The OGLE Collaboration
‡The µFUN Collaboration
♣The PLANET Collaboration
†The MOA Collaboration
and
⋆Corresponding author
Draft version October 10, 2013
ABSTRACT
We present a detailed analysis of survey and follow-up observations of microlensing event OGLE-2012-BLG-
0406 based on data obtained from 10 different observatories. Intensive coverage of the lightcurve, especially
the perturbation part, allowed us to accurately measure the parallax effect and lens orbital motion. Combining
our measurement of the lens parallax with the angular Einstein radius determined from finite-source effects,
we estimate the physical parameters of the lens system. We find that the event was caused by a 2.73±0.43 MJ
planet orbiting a 0.44±0.07M⊙early M-type star. The distance to the lens is 4.97±0.29kpc and the projected
separation between the host star and its planet at the time of the event is 3.45 ±0.26 AU. We find that the
additional coverage provided by follow-up observations, especially during the planetary perturbation, leads to
a more accurate determination of the physical parameters of the lens.
Subject headings: gravitational lensing – binaries: general – planetary systems
1. INTRODUCTION
Radial velocity and transit surveys, which primarily target
main-sequence stars, have already discovered hundreds of gi-
ant planets and are now beginning to explore the reservoir of
lower mass planets with orbit sizes extending to a few as-
tronomical units (AU). These planets mostly lie well inside
the snow line1of their host stars. Meanwhile, direct imag-
ing with large aperture telescopes has been discovering gi-
ant planets tens to hundreds of AUs away from their stars.
The region of sensitivity of microlensing lies somewhere in
between and extends to low-mass exoplanets lying beyond
the snow-line of their low-mass host stars, between ∼1 and
10 AU (Tsapras et al. 2003; Gaudi 2012). Although there
is already strong evidence that cold sub-Jovian planets are
more common than originally thought around low-mass stars
∗Royal Society University Research Fellow
1The snow line is defined as the distance from the star in a protoplanetary
disk where ice grains can form.
(Gould et al. 2006; Sumi et al. 2010; Kains et al. 2013), cold
super-Jupiters orbiting K or M-dwarfs were believed to be
a rarer class of objects2(Laughlin et al. 2004; Cassan et al.
2012).
The theoretical framework that underpins planetary forma-
tion scenarios that could potentially result in such systems in-
volves parameters that are currently too loosely constrained.
These parameters can be refined by tracing the distributions
of physical and orbital properties of a significant number of
planetary systems. The radial velocity method has been re-
markably successful in tabulating the part of the distribution
that lies within the snow-line but discoveries of super-Jupiters
beyond the snow-line of M-dwarfs have been comparatively
few (Johnson et al. 2010; Montet et al. 2013). By contrast,
this is exactly the type of planet that microlensing is most
sensitive to (Gaudi 2012).
2although a metal-rich protoplanetary disk might allow the formation of
sufficiently massive solid cores.

TSAPRAS ET AL. 3
Three brown dwarf and nineteen planet microlensing dis-
coveries have been published to date, including the dis-
coveries of two multiple-planet systems (Gaudi et al. 2008;
Han et al. 2013)3. It is also worth noting that unbound objects
of planetary mass have also been reported (Sumi et al. 2011).
Microlensing involves the chance alignment along an ob-
server’s line of sight of a foreground object (lens) and a back-
ground star (source). This results in a characteristic variation
of the brightness of the backgroundsource as it is being grav-
itationally lensed. As seen from the Earth, the brightness of
the source increases as it approaches the lens, reaching a max-
imum value at the time of closest approach. The brightness
then decreases again as the source moves away from the lens.
In microlensing events, planets orbiting the lens star can
reveal their presence through distortions in the otherwise
smoothly varying standard single lens lightcurve. Together,
the host star and planet constitute a binary lens. Binary lenses
have a magnification pattern that is more complex than the
single lens case due to the presence of extended caustics that
represent the positions on the source plane at which the lens-
ing magnification diverges. Distortions in the lightcurve arise
when the trajectory of the source star approaches (or crosses)
the caustics (Mao and Paczy´ nski 1991).
Upgrades to the OGLE4(Udalski 2003) survey observing
setup and MOA5(Sumi et al. 2003) microlensing survey tele-
scope in the past couple of years brought greater precision
and enhanced observing cadence, resulting in an increased
rate of exoplanet discoveries. For example, OGLE has reg-
ularly been monitoring the field of the OGLE-2012-BLG-
0406 event since March 2010 with a cadence of 55 minutes.
When a microlensing alert was issued notifying the astro-
nomical community that event OGLE-2012-BLG-0406 was
exhibiting anomalous behavior, intense follow-up observa-
tions from multiple observatories around the world were ini-
tiated in order to better characterize the deviation. This event
was first analyzed by Poleski et al. (2013) using exclusively
the OGLE-IV survey photometry. That study concluded that
the event was caused by a planetary system consisting of a
3.9±1.2 MJplanet orbiting a low mass late K/early M dwarf.
In this paper we present the analysis of the event based
on the combined data obtained from 10 different telescopes,
spread out in longitude, providing dense and continuous cov-
erage of the lightcurve.
The paper is structured as follows: Details of the discov-
ery of this event, follow-up observations and image analysis
procedures are described in Section 2. Section 3 presents the
methodology of modeling the features of the lightcurve. We
provide a summary and conclude in Section 4.
2. OBSERVATIONS AND DATA
Microlensing event OGLE-2012-BLG-0406 was discov-
ered at equatorial coordinates α= 17h53m18.17s,δ=
−30◦28′16.2′′ (J2000.0)6by the OGLE-IV survey and an-
nounced by their Early Warning System (EWS)7on the 6th
of April 2012. The event had a baseline I-band magnitude of
16.35 and was gradually increasing in brightness. The pre-
dicted maximum magnification at the time of announcement
was low, therefore the event was considered a low-priority
3For a complete list consult http://exoplanet.eu/catalog/ and references
therein.
4http://ogle.astrouw.edu.pl
5http://www.phys.canterbury.ac.nz/moa
6(l,b) = −0.46◦,−2.22◦
7http://ogle.astrouw.edu.pl/ogle4/ews/ews.html
target for most follow-up teams who preferentially observe
high-magnificationevents as they are associated with a higher
probability of detecting planets (Griest and Safizadeh 1998).
OGLE observations of the event were carried out with the
1.3-m Warsaw telescope at the Las Campanas Observatory,
Chile, equipped with the 32 chip mosaic camera. The event’s
field was visited every 55 minutes providing very dense and
precise coverage of the entire light curve from the baseline,
back to the baseline. For more details on the OGLE data and
coverage see Poleski et al. (2013).
An assessment of data acquired by the OGLE team un-
til the 1st of July (08:47 UT, HJD∼2456109.87) which
was carried out by the SIGNALMEN anomaly detector
(Dominik et al. 2007) on the 2nd of July (02:19 UT) con-
cluded that a microlensing anomaly, i.e. a deviation from
the standard bell-shaped Paczy´ nski curve (Paczy´ nski 1986),
was in progress. This was electronically communicated
via the ARTEMiS (Automated Robotic Terrestrial Exoplanet
Microlensing Search) system (Dominik et al. 2008) to trig-
ger prompt observations by both the RoboNet-II8collabo-
ration (Tsapras et al. 2009) and the MiNDSTEp9consortium
(Dominik 2010). RoboNet’s web-PLOP system (Horne et al.
2009) reacted to the trigger by scheduling observations al-
ready from the 2nd of July (02:30 UT), just 11 minutes af-
ter the SIGNALMEN assessment started. However, the first
RoboNet observations did not occur before the 4th of July
(15:26 UT), when the event was observed with the FTS. This
delayed response was due to the telescopes being offline for
engineering work and bad weather at the observing sites. It
fell to the Danish 1.54m at ESO La Silla to provide the first
data point following the anomaly alert (2nd of July, 03:42 UT)
as part of the MiNDSTEp efforts. The alert also triggered au-
tomated anomaly modeling by RTModel (Bozza 2010), which
by the 2nd of July (04:22 UT) delivered a rather broad variety
of solutions in the stellar binary or planetary range, reflecting
the fact that the true nature was not well-constrained by the
data available at that time. This process chain did not involve
any human interaction at all.
The first human involvement was an e-mail circulated to all
microlensing teams by V. Bozza on the 2nd of July (07:26 UT)
informing the community about the ongoing anomaly and
modeling results. Including OGLE data from a subsequent
night, the apparent anomaly was also independently spotted
by E. Bachelet (e-mail by D.P. Bennett of 3rd July, 13:42 UT),
and subsequently PLANET10 team (Beaulieu et al. 2006)
SAAO data as well as µFUN11 (Gould et al. 2006) SMARTS
(CTIO) data were acquired the coming night, which along
with the RoboNet FTS data cover the main peak of the
anomaly. It should be noted that the observers at CTIO de-
cided to follow the event even while the moon was full in
order to obtain crucial data. A model circulated by T. Sumi
on the 5th of July (00:38 UT) did not distinguish between the
various solutions.
However, when the rapidly changing features of the
anomaly were independently assessed by the Chungbuk Na-
tional University group (CBNU, C. Han), the community was
informed on the 5th of July (10:43 UT) that the anomaly is
very likely due to the presence of a planetary companion.
An independent modeling run by V. Bozza’s automatic soft-
8http://robonet.lcogt.net
9http://www.mindstep-science.org
10 http://planet.iap.fr
11 http://www.astronomy.ohio-state.edu/∼microfun

4 A REFINED ANALYSIS OF MICROLENSING EVENT OGLE-2012-BLG-0406
TABLE 1. OBSERVATIONS
group telescope passband data points
OGLE 1.3m Warsaw Telescope, Las Campanas Observatory (LCO), Chile I3013
RoboNet 2.0m Faulkes North Telescope (FTN), Haleakala, Hawaii, USA I83
RoboNet 2.0m Faulkes South Telescope (FTS), Siding Spring Observatory (SSO), Australia I121
RoboNet 2.0m Liverpool Telescope (LT), La Palma, Spain I131
MiNDSTEp 1.5m Danish Telescope, La Silla, Chile I473
MOA 0.6m Boller & Chivens (B&C), Mt. John, New Zealand I1856
µFUN 1.3m SMARTS, Cerro Tololo Inter-American Observatory (CTIO), Chile V,I16, 81
PLANET 1.0m Elizabeth Telescope, South African Astronomical Observatory (SAAO), South Africa I226
PLANET 1.0m Canopus Telescope, Mt. Canopus Observatory, Tasmania, Australia I210
WISE 1.0m Wise Telescope, Wise Observatory, Israel I180
ware (5th of July, 10:55 UT) confirmed the result. While the
OGLE collaboration(A. Udalski) notified observers on the 5th
of July that a caustic exit was occurring, a geometry leading
to a further small peak successively emerged from the mod-
els. D.P. Bennett circulated a model using updated data on
the 6th of July (00:14 UT) which highlighted the presence of
a second prominent feature expected to occur ∼10th of July.
Another modeling run performed at CBNU on the 7th of July
(02:39 UT) also identified this feature and estimated that the
secondary peak would occur on the 11th of July.
Follow-up teams continued to monitor the progress of the
event intensively until the beginning of September, well after
the planetary deviation had ceased, and provided dense cov-
erage of the main peak of the event. A preliminary model
using available OGLE and follow-up data at the time, circu-
lated on the 31st of October (C. Han, J.-Y. Choi), classified the
companion to the lens as a super-Jupiter. Poleski et al. (2013)
presented an analysis of this event using reprocessed survey
data exclusively. In this paper we present a refined analysis
using survey and follow-up data together.
The groups that contributed to the observations of this
event, along with the telescopes used, are listed in Table 1.
Most observations were obtained in the I-band and some im-
ages were also taken in other bands in order to create a color-
magnitude diagram and classify the source star. We note
that there are also observations obtained from the MOA 1.8m
survey telescope which we did not include in our modeling
because the target was very close to the edge of the CCD.
We also do not include data from the µFUN Auckland 0.4m,
PEST 0.3m, Possum 0.36m and Turitea 0.36m telescopes due
to poor observing conditions at site.
Extracting accurate photometry from observations of
crowded fields, such as the Galactic Bulge, is a challenging
process. Each image contains thousands of stars whose stellar
point-spread functions (PSFs) often overlap so aperture and
PSF-fitting photometry can at best offer limited precision. In
order to optimize the photometry it is necessary to use differ-
ence imaging (DI) techniques (Alard and Lupton 1998). For
any particular telescope/camera combination, DI uses a refer-
ence image of the event taken under optimal seeing conditions
which is then degraded to match the seeing conditions of ev-
ery other image of the event taken from that telescope. The
degraded reference image is then subtracted from the match-
ing image to produce a residual (or difference) image. Stars
that have not varied in brightness in the time interval between
the two images will cancel, leaving no systematic residuals
on the difference image but variable stars will leave either a
positive or negative residual.
DI is the preferred method of photometric analysis among
microlensing groups and each group has developed custom
pipelines to reduce their observations. OGLE and MOA im-
ages were reduced using the pipelines described in Udalski
(2003) and Bond et al. (2001) respectively. PLANET, µFUN,
and WISE images were processed using variants of the PySIS
(Albrow et al. 2009) pipeline, whereas RoboNet and MiND-
STEp observations were analyzed using customized versions
of the DanDIA package (Bramich 2008). Once the source star
returned to its baseline magnitude, each data set was repro-
cessed to optimize photometric precision. These photometri-
cally optimized data sets were used as input for our modeling
run.
3. MODELING
Figure 1 shows the lightcurve of OGLE-2012-BLG-406.
The lightcurve displays two main features that deviate signif-
icantly from the standard Paczy´ nski curve. The first feature,
which peaked at HJD ∼2456112 (3rd of July), is produced
by the source trajectory grazing the cusp of a caustic. The
brightness then quickly drops as the source moves away from
the cusp, increases again for a brief period as it passes close to
another cusp at HJD ∼2456121 (12th of July), and eventually
returns to the standard shape as the source moves further away
from the caustic structure. The anomalous behavior, when
both features are considered, lasts for a total of ∼15 days,
while the full duration of the event is &120 days. These are
typical lightcurve features expected from lensing phenomena
involving planetary lenses.
We begin our analysis by exploring a standard set of solu-
tions that involve modeling the event as a static binary lens.
The Paczy´ nski curve representing the evolution of the event
for most of its duration is described by three parameters: the
time of closest approach between the projected position of the
source on the lens plane and the position of the lens photo-
center12,t0, the minimum impact parameter of the source, u0,
expressed in units of the angular Einstein radius of the lens
(θE), and the duration of time, tE(the Einstein time-scale), re-
quired for the source to cross θE. The binary nature of the lens
requires the introduction of three extra parameters: The mass
ratio qbetween the two components of the lens, their pro-
jected separation s, expressed in units of θE, and the source
trajectory angle αwith respect to the axis defined by the two
12 The "photocenter" refers to the center of the lensing magnification pat-
tern. For a binary-lens with a projected separation between the lens compo-
nents less than the Einstein radius of the lens, the photocenter corresponds
to the center of mass. For a lens with a separation greater than the Einstein
radius, there exist two photocenters each of which is located close to each
lens component with an offset q/[s(1+q)] toward the other lens component
(Kim et al. 2009). In this case, the reference t0,u0measurement is obtained
from the photocenter to which the source trajectory approaches closest.

TSAPRAS ET AL. 5
FIG. 1.— Lightcurve of OGLE-2012-BLG-0406 showing our best-fit binary-lens model including parallax and orbital motion. The legend on the right of the
figure lists the contributing telescopes. All data were taken in the I-band, except where otherwise indicated.
TABLE 2. LENSING PARAMETERS
parameters standard parallax orbit orbit+parallax
u0>0u0<0u0>0u0<0u0>0u0<0
χ2/dof 6921.019/6383 6850.358/6381 6677.685/6381 6408.371/6381 6408.255/6381 6357.680/6379 6381.358/6379
t0(HJD’) 6141.63 ±0.04 6141.70 ±0.05 6141.66 ±0.05 6141.24 ±0.05 6141.28 ±0.04 6141.33 ±0.05 6141.19 ±0.06
u00.532 ±0.001 0.527 ±0.001 -0.520 ±0.001 0.500 ±0.002 -0.499 ±0.002 0.496 ±0.002 -0.497 ±0.002
tE(days) 62.37 ±0.06 63.75 ±0.18 69.39 ±0.32 65.33 ±0.20 65.53 ±0.15 64.77 ±0.19 61.91 ±0.42
s1.346 ±0.001 1.345 ±0.001 1.341 ±0.001 1.300 ±0.002 1.301 ±0.001 1.301 ±0.002 1.296 ±0.002
q(10−3) 5.33 ±0.04 5.07 ±0.03 4.45 ±0.04 6.97 ±0.27 6.63 ±0.05 5.92 ±0.11 6.82 ±0.19
α0.852 ±0.001 0.864 ±0.002 -0.906 ±0.002 0.861 ±0.002 -0.859 ±0.001 0.837 ±0.002 -0.810 ±0.005
ρ∗(10−2) 1.103 ±0.008 1.053 ±0.007 0.968 ±0.009 1.233 ±0.031 1.194 ±0.011 1.111 ±0.014 1.207 ±0.023
πE,N– 0.118 ±0.011 -0.414 ±0.016 – – -0.143 ±0.018 0.358 ±0.042
πE,E– -0.033 ±0.007 -0.069 ±0.009 – – 0.047 ±0.007 0.008 ±0.006
ds/dt (yr−1) – – – 0.765 ±0.046 0.727 ±0.017 0.669 ±0.028 0.802 ±0.033
dα/dt (yr−1) – – – 1.284 ±0.159 -1.108 ±0.019 0.497 ±0.059 -0.732 ±0.085
NOTE. — HJD’=HJD-2450000.
componentsof the lens. A seventh parameter,ρ∗, representing
the source radius normalized by the angular Einstein radius
is also required to account for finite-source effects that are
important when the source trajectory approaches or crosses a
caustic.
The magnification pattern produced by binary lenses is very
sensitive to variations in s,q, which are the parameters that
affect the shape and orientation of the caustics, and α, the
source trajectory angle. Even small changes in these param-
eters can produce extreme changes in magnification as they
may result in the trajectory of the source approaching or cross-
ing a caustic. On the other hand, changes in the other parame-
ters cause the overall magnification pattern to vary smoothly.
To assess how the magnification pattern depends on the pa-
rameters, we start the modeling run by performing a hybrid
search in parameter space whereby we explore a grid of s,q,α
values and optimize t0,u0,tEand ρ∗at each grid point by
χ2minimization using Markov Chain Monte Carlo (MCMC).
Our grid limits are set at −1≤logs≤1, −5≤logq≤1, and
0≤α < 2π, which are wide enough to guarantee that all local
minima in parameter space have been identified. An initial
MCMC run provides a map of the topology of the χ2surface,
which is subsequently further refined by gradually narrow-
ing down the grid parameter search space (Shin et al. 2012a;
Street et al. 2013). Once we know the approximate locations
of the local minima, we perform a χ2optimization using all